U.S. Pat. No. 5,211,177 (incorporated herein by reference) discloses method and apparatus for measuring properties of the human vasculature using an electrical analog model of vascular impedance. These properties include the compliance of large and small vessels, and systemic resistance. These measurements and others obtained from the model can in turn be used to diagnose states of health or disease, and to assess the effectiveness of treatment regimes. For example, see Finkelstein S. M., Collins V. R., Cohn J. N., Arterial vascular compliance response to vasodilators by Fourier and pulse contour analysis, Hypertension 1988:12:380-387, the entire disclosure of which is incorporated herein by reference.
The simplest model for representing the time-varying pressure behavior of the arterial blood pressure waveform during the diastolic decay phase of the cardiac cycle is a first-order model. The analog model that represents this behavior contains a single "active" element (capacitance) and a passive element (resistance). The model only accounts for the pure exponential decay present in the waveform. An improvement to this model that better accounts for the observed shape of the diastolic decay in humans is a third-order model, for example, the modified Windkessel model. The analog model that represents this behavior contains three active elements, two capacitors (compliance) separated by an inductor (inertance of the blood) and a passive resistance (systemic vascular resistance) element. This is the model preferred in the system of U.S. '177, and employed in the approach of the example embodiment of the present invention described herein.
U.S. '177 describes a time-domain pulse contour analysis employed to extract useful information from the arterial blood pressure waveform. This pulse contour analysis employs a curve fitting approach applied to the diastolic blood pressure decay and subsequent use of the modified Windkessel electrical analog model of the vasculature to give physiological meaning to the analysis in terms of measures of systemic arterial performance.
The modified Windkessel model of the arterial system is shown in FIG. 1. The model includes components P.sub.1, P.sub.2, C.sub.1, C.sub.2, L and R in which:
C.sub.1 =proximal or capacitive compliance (ml/mm Hg) PA1 C.sub.2 =distal or reflective or oscillatory compliance (ml/mm Hg) PA1 L=inertance (mm Hg/(ml/s.sup.2)) PA1 P.sub.1 =proximal or aortic arterial pressure (mm Hg) PA1 P.sub.2 =distal or peripheral artery pressure (mm Hg) PA1 R=peripheral resistance (dynes s cm.sup.-5)
As taught, for example, by Goldwyn and Watt in I.E.E.E. Trans. Biomed. Eng. 1967; 14:11-17, the disclosure of which is hereby incorporated by reference herein, P.sub.2 of the modified Windkessel model may be represented by the third order equation: EQU P(t)=A.sub.1 e.sup.-A.sbsp.2.sup.t +A.sub.3 e.sup.-A.sbsp.4.sup.t cos(A.sub.5 t+A.sub.6)
wherein: ##EQU1## EQU m=A.sub.2 +2A.sub.4 EQU n=2A.sub.2 A.sub.4 +A.sub.4.sup.2 +A.sub.5.sup.2
and EQU p=A.sub.2 (A.sub.4.sup.2 +A.sub.5.sup.2)
Thus, knowing R, which can be calculated from cardiac output and mean arterial pressure as follows: ##EQU2## C.sub.1, C.sub.2 and L are readily calculated.
Pulse contour analysis as described in U.S. '177 begins with the acquisition of digital representation of the arterial waveform. A number of consecutive beats are acquired, preferably for about 30 seconds, and stored for processing. These beats are then screened to eliminate abnormally fast or slow beats, or beats of abnormally high or low pressure. This screening preferably yields at least six to ten consecutive beats to be used for further analysis. Using a software algorithm, this representation is then marked to identify the diastolic portion of the arterial blood pressure waveform.
In U.S. '177, a curve fitting algorithm, such as the Gauss-Newton parameter estimating algorithm, is then applied to the marked diastolic data set of the waveform to ascertain the `A` coefficients of the modified Windkessel model. An automatic stopping procedure was employed to stop iteration when an acceptable level of error was reached or when convergence slowed below a preset threshold. Also, U.S. '177 proposed that when the process started to diverge it returned to the previous best case. Additionally, the routine included a weighted iteration interval to improve convergence. Using a measure of cardiac output and mean arterial pressure to calculate R, the modified Windkessel parameters C.sub.1, C.sub.2 and L could then be calculated as well. In U.S. '177, it is contemplated that the parameters R, C.sub.1, C.sub.2 and L are calculated for each beat in the set under analysis, and subsequently averaged to produce mean values more reliable for accuracy than any of the individual values. Alternatively, U.S. '177 teaches that median values can be selected.
While the approach taught in U.S. '177 produces useful results, it has been a goal of researchers to continue to perfect and improve waveform analysis, in order to more reliably obtain measurements of vascular impedance. To this end, a number of areas for improvement have been identified and presented herein.